Note on the space group selection rule for closed strings on orbifolds

It is well-known that the space group selection rule constrains the interactions of closed strings on orbifolds. For some examples, this rule has been described by an effective Abelian symmetry that combines with a permutation symmetry to a non-Abelian flavor symmetry like $D_4$ or $\Delta(54)$. However, the general case of the effective Abelian symmetries was not yet fully understood. In this work, we formalize the computation of the Abelian symmetry that results from the space group selection rule by imposing two conditions only: (i) well-defined discrete charges and (ii) their conservation. The resulting symmetry, which we call the space group flavor symmetry $D_S$, is uniquely specified by the Abelianization of the space group. For all Abelian orbifolds with $N=1$ supersymmetry we compute $D_S$ and identify new cases, for example, where $D_S$ contains a $Z_2$ dark matter-parity with charges 0 and 1 for massless and massive strings, respectively.Comment: 28 pages, 1 tabl

Grand Unification in the Heterotic Brane World

The compactification of the heterotic string on six-dimensional orbifolds is reviewed. Some important technical aspects of their construction are clarified and new parameters, called generalized discrete torsion, are introduced and related to the torsionless construction. Furthermore, a systematic search for MSSM-like models is performed in the context of Z6-II orbifolds, addressing questions like the identification of a supersymmetric vacuum with a naturally small mu-term and proton decay. Finally, the blow-up of Z3 singularities is discussed in the local and in the global case - also in the presence of Wilson lines. This procedure is exemplified with the resolution of a Z3 MSSM candidate.Comment: 134 pages, Ph.D. Thesis (Advisor: Hans Peter Nilles

Infinite number of MSSMs from heterotic line bundles?

We consider heterotic E8xE8 supergravity compactified on smooth Calabi-Yau manifolds with line bundle gauge backgrounds. Infinite sets of models that satisfy the Bianchi identities and flux quantization conditions can be constructed by letting their background flux quanta grow without bound. Even though we do not have a general proof, we find that all examples are at the boundary of the theory's validity: the Donaldson-Uhlenbeck-Yau equations, which can be thought of as vanishing D-term conditions, cannot be satisfied inside the Kaehler cone unless a growing number of scalar Vacuum Expectation Values (VEVs) is switched on. As they are charged under various line bundles simultaneously, the gauge background gets deformed by these VEVs to a non-Abelian bundle. In general, our physical expectation is that such infinite sets of models should be impossible, since they never seem to occur in exact CFT constructions.Comment: LaTeX, 8 pages, 4 tables, some references and comments adde

CP\mathcal{CP} Violation from String Theory

We identify a natural way to embed $\mathcal{CP}$ symmetry and its violation in string theory. The $\mathcal{CP}$ symmetry of the low energy effective theory is broken by the presence of heavy string modes. $\mathcal{CP}$ violation is the result of an interplay of $\mathcal{CP}$ and flavor symmetry. $\mathcal{CP}$ violating decays of the heavy modes could originate a cosmological matter-antimatter asymmetry.Comment: 7 pages, 4 figure

Mirage Torsion

Z_NxZ_M orbifold models admit the introduction of a discrete torsion phase. We find that models with discrete torsion have an alternative description in terms of torsionless models. More specifically, discrete torsion can be 'gauged away' by changing the shifts by lattice vectors. Similarly, a large class of the so-called generalized discrete torsion phases can be traded for changing the background fields (Wilson lines) by lattice vectors. We further observe that certain models with generalized discrete torsion are equivalent to torsionless models with the same gauge embedding but based on different compactification lattices. We also present a method of classifying heterotic Z_NxZ_M orbifolds.Comment: 26 pages, 3 figures, v2: matches version published in JHE

Singlet Extensions of the MSSM with Z(4)(R) Symmetry

We discuss singlet extensions of the MSSM with Z(4)(R) symmetry. We show that holomorphic zeros can avoid a potentially large coefficient of the term linear in the singlet. The emerging model has both an effective mu term and a supersymmetric mass term for the singlet mu(N) which are controlled by the gravitino mass. The mu term turns out to be suppressed against mu(N) by about one or two orders of magnitude. We argue that this class of models might provide us with a solution to the little hierarchy problem of the MSSM